CAT QUANT NUMBER SYSTEM 7

If a three digit number 'abc' has 3 factors, how many factors does the 6 digit number 'abcabc' have?

Find the smallest number that has exactly 18 factors.

Number $\mathrm{N}=2^{6} \times 5^{5} \times 7^{6} \times 10^{7}$; how many factors of $\mathrm{N}$ are even numbers?

If a three digit number 'abc' has 2 factors (where $a, b, c$ are digits), how many factors does the 6 -digit number 'abcabc' have?

Numbers $A, B, C$ and $D$ have $16,28,30$ and $27$ factors. Which of these could be a perfect cube?

A number $\mathrm{N}^{2}$ has 15 factors. How many factors can $\mathrm{N}$ have?

A number when divided by 18 leaves a remainder 7 . The same number when divided by 12 leaves a remainder $\mathrm{n}$. How many values can $\mathrm{n}$ take?

What is the remainder when $\left(13^{100}+17^{100}\right)$ is divided by $25 ?$

The sum of the digits of a number $N$ is 23 . The remainder when $N$ is divided by 11 is 7 . What is the remainder when $\mathrm{N}$ is divided by 33 ?

How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1 ?